New constitutive relationships for hyperelastic transversely isotropic materials have been proposed. The well-known isotropic hyperelastic model due to OGDEN 11.581 has been extended to transverse isotropy. It has been shown that some models intended to describe the nonlinear elastic behaviour of soft tissues are oversimplified and lead to incorrect results. An overview of soft tissue modelling, being a continuation of the one started in [481, has also been given.